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Radial and Transverse Forces Beer and Johnston 9th ed. 12.70

  1. Oct 11, 2011 #1
    1. The problem statement, all variables and given/known data

    The 3 kg collar B slides on the frictionless arm AA'. The arm is attached to drum D and rotates about O in a horizontal plane at the rate dθ/dt = 0.75t, where dθ/dt and t are expressed in rad/s and seconds, respectively. As the arm-drum assembly rotates, a mechanism within the drum releases cord so that the collar moves outward from O with a constant speed of 0.5 m/s. Knowing that at t = 0, r = 0, determine the time at which the tension in the cord is equal to the magnitude of the horizontal force exerted on B by arm AA'.

    2. Relevant equations

    Fr = m(d2θ/dt2 - r(dθ/dt)2)
    Fθ = m(rd2θ/dt2 + 2(dr/dt)(dθ/dt))
    ƩF = ma

    3. The attempt at a solution

    Fr = -T
    r = (0.5 m/s)t
    dr/dt = 0.5 m/s
    d2r/dt = 0 m/s2
    dθ/dt = (0.75 m/s)t
    d2θ/dt = 0.75 m/s2

    Fr = 3 kg(0 - 0.5t(0.75t)2)
    Fr = -0.844t3

    Fθ = 3 kg(0.5t(.75) + 2(0.5)(0.75t))
    Fθ = 3.375t

    Now if Fr = -T then I can substitute -T for Fr. Therefore
    T = 0.844t3

    I'm not sure where to go after this one.. I need to somehow solve for t I know that but I'm just not sure because I have two equations and three unknowns.

    Thanks ahead of time for any help.
  2. jcsd
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